A fourth-order degenerate parabolic equation describing thin viscous flows over an inclined plane
The author proves existence of nonnegative weak solutions for the fourth-order nonlinear degenerate parabolic equation \[ u_t+[u^n(b-cu_x+u_{xxx})]_x=0 \] which arises in the description of thin viscous flows over an inclined plane. Regularity, positivity and large-time behavior of these solutions are discussed as well.
regularity, positivity and large-time behavior
scientific article; zbMATH DE number 1428537